Question

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Answer 1

Answer:

let 12 spheres have radius r

∴ by volume conservation 12 x 4/3 πr^3=πR^2h

from here r=1cm then d= 2cm

Answer 2

Step-by-step explanation:

Question:-

12 spheres of same volumes are recasted by a melting a cylinder solid with a base diameter 2cm and height 16cm. The diameter of each sphere is:-

Solution:-

Let the radius of a sphere be ' r '

Volume of the sphere = $\dfrac{4}{3}$ πr³

Volume of 12 spheres:-

= $\dfrac{4}{3}$ × 12 × πr³

= 4 × 4 × πr³

= 16πr³

Volume of 12 spheres = 16πr³

Given, Base diameter of cylinder = 2cm

Radius of the cylinder (R) = 1cm

Height of the cylinder = 16cm

Volume of the cylinder = πR²h

= π × (1)² × 16

= 16π

Volume of the cylinder = 16π

As, Volume of 12 spheres = Volume of cylinder

→ 16πr³ = 16π

→ r³ = $\dfrac{16\pi}{16\pi}$

→ r³ = 1

→ r = $\sqrt[3]{1}$ = 1cm

Radius of each sphere = 1cm

∴ Diameter of each sphere recasted = 2cm